Proceedings on Engineering Sciences SELECTING LEAN SIX

1 Corresponding author: Ufuk Cebeci

Email: [email protected] 223

Vol. 02, No. 3 (2020) 223-236, doi: 10.24874/PES02.03.002

Proceedings on Engineering

Sciences

www.pesjournal.net

SELECTING LEAN SIX SIGMA MANAGER BY

USING TYPE-2 FUZZY AHP WITH A REAL CASE

APPLICATION IN A LOGISTICS FIRM

Ufuk Cebeci1

Keywords:

Type 2 fuzzy AHP; Lean six sigma;

MCDM; Manager Selection; Logistics.

A B S T R A C T

The aim of this study is to develop a framework for Selecting Lean Six Sigma

Manager among candidates by using Type-2 Fuzzy Sets. Some authors found

that the management of six sigma projects and management’s commitment are

very important for the prevention of failure of them. Since the problem of

selection of lean six sigma manager has various and conflicting criteria, it is a

Multi Criteria Decision Making problem. The trapezoidal interval type-2 fuzzy

Analytic Hierarchy Process methodology, which is one of the most used

methods, is applied for an industrial manager selection. The membership

functions of type-1 fuzzy sets are two-dimensional, whereas the membership

functions of type-2 fuzzy sets are three-dimensional. It is the new third-

dimension that provides additional degrees of freedom that make it possible to

directly model uncertainties. There is no study about the selection of lean six

sigma manager in literature. Logistics industry is one of the most important

sectors for employment all over the world. Some logistics companies are visited

and studied their processes carefully. In Lean Six Sigma Manager selection

process, there are multiple criteria to consider and many candidates. In order

to put those linguistic criteria in numerical presentation and ranking, AHP is a

widely used MCDM tool. In this paper, the proposed criteria are leadership

(C1), sectoral expertise (C2), personal and environmental analysis ability (C3),

education (C4).

© 2020 Published by Faculty of Engineering

1. INTRODUCTION

The aim of this study is to develop a framework for

Selecting Lean Six Sigma Manager by using Type-2

Fuzzy Sets. The trapezoidal interval type-2 fuzzy

Analytic Hierarchy Process methodology is applied for

an industrial manager selection. The key resource of a

modern organization is human resources. People make

differences in today’s global business and economy. The

performance of a Lean six sigma manager can effect

almost every critical processes in a company, because

lean six sigma projects focus the problematic processes,

bottlenecks, and the most important processes to be

improved. The author has not seen any study about the

selection of a lean six sigma manager. If the selection of

a manager fails it will yield too much expenses and waste

of time and resources. Because of different difficulties, it

is hard to find a perfect method for recruitment and

selection.

Lean Six Sigma concept started to be used in year 2000

as an integration of Six Sigma and Lean Manufacturing

by Sheridan (2000). Before year 2000, two concepts are

used independently. Taiichi Ohno founded first lean

Cebeci, Proceedings on Engineering Sciences, Vol. 02, No. 3 (2020) 223-236, doi: 10.24874/PES02.03.002

224

manufacturing techniques in 1950s, Toyota Japan. Lean

manufacturing is called Toyota production system, which

included continuous search to eliminate waste (Japanese

word is called Muda), the involvement of employees to

improve their processes, to reduce inventory level,

increase productivity, to prevent late deliveries, to solve

the problem of bottleneck machines or operations, one

piece a time production, the satisfied customers, smooth

flow of a production or service system like a river, etc.

Womack and Jones (1996) state lean manufacturing as “a

way to specify value, line up value-creating actions in the

best sequence, conduct those activities without

interruption whenever someone requests them, and

perform them more and more effectively. In short, lean

thinking is lean because it provides a way to do more and

more with less and less – less human effort, less human

equipment, less time, and less space – while coming

closer and closer to providing customers with exactly

what they want.”

It is possible to deliver products in time, at a lower cost

by using lean manufacturing continuous improvement

techniques.

Motorola sold its TV factory to a Japan company. The

new management of the company achieved zero defect

quality level, soon with the same employees and without

buying new technology machines. Then Bill Smith,

Motorola Engineer defined a quality control process and

obtained successful results. Later, Motorola defined the

approach as Six Sigma and registered this concept. Six

sigma stages are Define, Measure, Analyze, Improve,

and Control (DMAIC) and six sigma has some

similarities of PDCA (Plan, Do, Control and Act) of

Kaizen (continuous improvement cycle) which is a

component of Total Quality Management. General

Electric (GE) is one of the pioneering firms applying six

sigma. GE group explained that they saved more money

in group’s service companies such as banking or

insurance industry than production companies after

applying six sigma projects.

Snee (1999) focused the importance of statistics and

described six sigma as “a business strategy that seeks to

identify and eliminate causes of errors or defects or

failures in business processes by focusing on outputs that

are critical to customers”.

Every company can apply lean six sigma techniques. In

literature, it is possible to see a lot of the applications of

lean six sigma; SME (small medium size enterprise) or

big, domestic or local. In addition, every sector can apply

lean six sigma projects. Some examples in literature are:

Logistics services by Gutierrez-Gutierrez et al.

(2016).

A pharmaceutical firm study By Pavlovic and

Bozanic (2012).

Family Drug Courts Information Sharing by

Kovach et al. (2017).

Klochkov et al. (2019) present various lean

performance characteristics with a case study

from a water pump producer for sustainable

business process.

Hospital applications; in medical records

department of a hospital in India by Bhat et al.

(2016) and operating room efficiency of a

university students hospital by Tagge et al.

(2017).

The questionnaire of the logistics firms

registered by Singapore Logistics Association

by Zhang et al. (2016).

- Carvalho et al. (2017) review logistics

applications in a systematic way. - The

implementation methodology of lean six sigma

in supply chain management suggested by Salah

and Rahim (2019).

Telecom industry application for mobile orders

by Shamsuzzaman et al. (2018).

Banking industry by Muturi et al. (2015), textile by

Adikorley et al. (2017), construction by Fernández-Solís,

and Gadhok (2018), ship building by Jiang et al. (2016)

etc. almost every sector studies can be found in literature.

It is an important concept for both production companies

and service companies. Albliwi et al. (2014), after

reviewing 56 papers, report that there are some common

reasons for the failure such as lack of top management

commitment and involvement, lack of communication,

lack of training and education. Zimmerman and Weiss

(2005) state that less than 50% from aerospace

companies were satisfied with its Six Sigma programs

according to their survey results. Chakravorty (2009)

referenced that two human issues relevant for Six Sigma

failures are selective perception and illusion of control.

Hastorf and Cantril (1954, p.133), a person selects those

that have some significance for him from his own

egocentric position in the total matrix.” Selective

perception is not an individual trait, but is the product of

individual experience and the situation at hand (Hogarth

1987).

Dearborn and Simon (1958) found managers perceive

information according to their functional background.

The flow of the paper is as follows:

The evaluated criteria for hiring six sigma

manager

Type-2 fuzzy AHP

The developed framework and an industrial case

study in an international logistics company

Conclusion and future study.

2. CRITERIA FOR HIRING LEAN SIX

SIGMA MANAGER

Marzagão and Carvalho (2016) study critical success

factors of six sigma projects and apply a survey in Brazil

and Argentina with 149 respondents. Their model shows


225

that Manager, project management and six sigma

techniques used for the selected problem are very

important for the success of six sigma projects. The study

of Marzagão and Carvalho (2016) shows the importance

of the selection lean six sigma manager which the author

of this paper focuses the personnel selection topic for lean

six sigma. Because improper manager may focus wrong

priorities and cannot use the right techniques.

There are a lot of six sigma project selection studies in

literature (Adebanjo et al. 2016, Ortíz et al. 2015).

However, the author of this paper has not seen any study

about the selection of lean six sigma manager. If a wrong

manager is selected, the decision may affect the success

of all lean six sigma projects and the motivation and

moral of the employees in the organization. Business

professionals and academics believe that the process of

personnel selection should be on justice and with

minimum subjectivity.

Rahim et al. (2018) suggest a methodology for selecting

best employee by using TOPSIS method. This study is

applied for the selection of already working employees in

a firm. They consider “Job Responsibilities, Work

Discipline, Work Quality, and Behavior” criteria.

Hababou and Martel (1998) study portfolio manager

selection by using MCDM, The PROMETHEE II. They

defined some criteria. One of them, which is related to

this study is “past performance”.

Laureani and Antony (2019) review the papers, published

in 97 journals, about lean six sigma and leadership. The

most publishing ones are Quality Progress, International

Journal of Quality & Reliability Management,

International Journal of Six Sigma and Competitive

Advantage, Harvard Business Review and Total Quality

Management & Business Excellence.

Raymond et al. (2006) study sales managers and

representatives and their study explores that managers

believe objective assessment, technical skills,

experiential learning, acquired skills, college

accomplishments, and extracurricular activities are more

important.

Young and Lee (1997) analyzed the Information System

Graduate candidate selection process. After applying the

questionnaire, respondent managers state top 3 ranked

hiring criteria by using the below criteria:

1- Grade point average (GPA).

2-Problem-solving skills.

3-Written and oral communications skills.

4-Leadership through extracurricular activities.

5-Self-confidence and poise during the interview

process.

6-Internship or other full-time work experience.

7-Technical skills.

Bills (1992) reported employers believe to hire

overqualified personnel, because they may achieve

carrier targets more easily. According to Bunderson and

Sutcliffe (1995), functional boundaries tend to restrict a

manager’s view of a problem. The criteria are determined

by decision makers (sector expert top manager,

academics) and literature; Hababou and Martel, (1998),

Raymond et al. (2006), Young and Lee (1997), Albliwi

et al. (2014), Bunderson and Sutcliffe (1995). The criteria

are as follows:

Leadership

Sectoral Expertise

Personal and Environmental Analysis Ability

Education.

Leadership: This concept is very important for the

success of Lean Six Sigma applications. Lean Six Sigma

Manager (LSSM) needs to be involved the employees,

and to increase their motivation.

Sectoral Expertise: It is another important skill to

understand the processes of the company and sector. The

manager can see the inputs and outputs of the system

easily, and have the empathy, if he or she has a sectoral

expertise. Some professionals have only the theoretical

background of statistics used in six sigma; therefore, they

cannot understand the problems of real world.

Personal and Environmental Analysis Ability: This skill

is important to build the model to solve the problem by

using analysis skill.

Education: If the manager knows statistical techniques,

lean concepts from university education, he or she can

understand why and how necessary these techniques are.

Because, sometime we meet some lean six sigma users,

even consultants that they can solve a lean six sigma

problem but they do not know the knowledge behind six

sigma. If the model of the problem is somewhat different,

they cannot solve the problem correctly. Industrial

engineers or industrial & system engineers may have an

advantage for the title of lean six sigma manager, because

they learn statistics focused lean six sigma and Total

Quality Management, in addition, how a service system

or manufacturing system works at their universities.

One of the highly used methods for Multi Criteria

Decision Making (MCDM) is Analytic Hierarchy

Process (AHP); in which, the most suitable alternatives

are found for a defined problem. While the membership

functions of type-1 fuzzy sets are two-dimensional, the

membership functions of type-2 fuzzy sets are three-

dimensional. It is the new third dimension that provides

additional degrees of freedom that make it possible to

directly model uncertainties.

Runkler et al (2017) focused on risk by considering

interval type-2 fuzzy sets and applied a traffic problem

example and the improved results are % 8-5 better

decisions.


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Görener et al (2017) present a holistic approach for

vendor evaluation in an aviation maintenance industry.

They use type 2 fuzzy including tangible and intangible

evaluation criteria.

Özkan et al. (2015) applied a hybrid multicriteria

decision making methodology based on type-2 fuzzy sets

to select among energy storage alternatives.

Cebeci (2018) applied type 2 fuzzy AHP for Manager

Selection, and JCI (Joint Commission International, a

very common hospital quality management standard

developed in USA) consultant selection by using fuzzy

AHP (Cebeci, 2009).

Hmoud and Lazslo (2019) review and predict Human

Resources Recruitment in Artificial Intelligence and

argue that Ariticial Intelligence can be used for some

routine positions and applications such as sourcing and

screening. When a big company search a huge number of

candidates as employees or intern, this routine task can

be done by AI software quickly and effectively.

A number of studies by using MCDM techniques for the

selection of personnel are done by different authors such

as Saaty’s AHP (1977), Liang and Wang (1994), Saaty’s

ANP method (1996).

Gungor et al. (2009) applied Fuzzy Analytic Hierarchy

Process to the problem of personnel selection and they

compared to the results of Yager’s weighted goals

method.

Petrovic-Lazarevic (2001) applied to the problem of

personnel selection “senior economic and financial

analyst” and developed a software and use it for the

calculations.

Özdağoğlu and Özdağoğlu (2007) applied fuzzy AHP

and AHP methods and compared the results for the

selection of shop floor workers.

Karabasevic et al. (2016) proposed a framework and used

fuzzy MCDM SWARA (Step-wise Weight Assessment

Ratio Analysis) method and ARAS (Additive Ratio

Assessment) method for the selection of sales manager.

They used SWARA for the determination of weighting

factors and ARAS for the ranking alternatives of the sales

person candidates.

2.1 Type-2 fuzzy AHP

The fuzzy set theory was introduced first by Zadeh

(1965). A major contribution of fuzzy set theory is its

capability of representing vague data. The theory also

allows mathematical operators and programming to

apply to the fuzzy domain. Fuzzy sets can convert a

human’s experience and judgment to quantitative data.




are found for a defined problem.

Classical AHP is a subjective method and form

unbalanced judgement scale. Fuzzy AHP is used very

commonly, because it can reflect human thinking style,

whereas classical AHP cannot reflect. Fuzzy AHP can

be used to prevent this risk. Özdağoğlu and Özdağoğlu

(2007) concluded that “Some pessimistic people may not

give any point more than four, or very optimistic people

may easily give 5 even if it does not deserve it. These

situations generate fuzziness within the decision making

process, so fuzzy AHP method can handle these

deviations concerning this fuzziness. Therefore, for the

employee selection problems, if a multi-criteria decision

making method with linguistic evaluations is selected,

this method can be fuzzy AHP or similar methods

concerning fuzzy conditions.”

The membership functions of type-1 fuzzy sets are crisp;

therefore, they cannot model uncertainties directly. But

the membership functions of type-2 fuzzy sets are fuzzy,

they can model uncertainties.

Kahraman et al., (2014) developed trapezoidal interval

type-2 fuzzy AHP method together with a new ranking

method for type-2 fuzzy sets and applied the proposed

method to a supplier selection problem.

While the membership functions of type-1 fuzzy sets are

two-dimensional, the membership functions of type-2

fuzzy sets are three-dimensional. It is the new third-

dimension that provides additional degrees of freedom

that make it possible to directly model uncertainties.

An interval type-2 fuzzy set is a special case of a

generalized type-2 fuzzy set. Since generalized type-2

fuzzy sets require complex and immense computational

burdensome operations, the wide spread application of

generalized type-2 fuzzy systems has not occurred.

Interval type-2 fuzzy sets are the most commonly used

type-2 fuzzy sets because of their simplicity and reduced

computational effort with respect to general type-2 fuzzy

sets.

In this paper, the trapezoidal interval type-2 fuzzy

Analytic Hierarchy Process methodology is applied to

the problem of the industrial manager selection of lean

six sigma.

3. DEVELOPED FRAMEWORK AND AN

INDUSTRIAL CASE STUDY APPLIED IN

LOGISTICS SECTOR

Logistics industry is one of the most important sectors for

employment all over the world. Turkey’s advantageous

geographical location that stretches from Asia to Europe

and Russia to Africa, allows it to be a hub for over USD

2 trillion freight carried in the region.


227

Turkey (LODER), Turkey’s current logistics industry

size is estimated to be USD 80-100 billion and is forecast

to reach USD 108-140 billion by 2017. A strong and

diversified economy will contribute to the expansion of

the logistics industry. Since many industries support or

rely on the logistics industry, their growth would

indirectly stimulate growth in logistics. Global logistics

players are keen to invest in Turkey because of the

growth potential within the Turkish economy and its

proximity to Europe and Asia. Turkey has already

attracted big global players.

The Lean Six Sigma Manager Candidate Selection Flow

Chart is shown in Figure 1.

Figure 1. Lean Six Sigma Manager Candidate Selection Flow Chart

Turkey is building logistics centers/villages that will

serve to lower the costs of transportation by offering

various different modes of transportation within these

centers/villages. It is estimated that by 2023, total freight

carried in the centers/villages will reach a total of USD

500 billion. [www.invest.gov.tr/enUS/infocenter/

publications/Documents/TRANSPORTATION-

LOGISTICS-INDUSTRY.pdf] Turkey has a population

of 76 million people and is growing with rising income

levels. This makes Turkey one of the largest markets in

its region, and the changing consumer habits of the

younger generation boost domestic consumption.

Organizations are continuously looking for the new ways

to improve their performance and stay competitive in


228

their markets. Some logistics companies are visited and

studied their processes carefully. The logistics firms

visited are Hedef Logistics, Imser Logistics, TTS

Logistics.Two software house (Select:

http://www.selectyazilim.com and Kesit,

www.kesit.info), expert about logistics software are

visited and analyzed their software. Information About

The Company: NMT Logistics company

(http://www.nmtlojistik.com/en) was chosen to apply

this study (type-2 Fuzzy AHP for selecting and hiring

Lean Six Sigma Manager), because of top management’s

commitment. NMT Logistics, established in 2007, is a

company operating in the area of supply chain

management and international transportation, having R2

certificate, ISO 9001 quality management system

cetificate and is a member of The Turkish Chamber of

Shipping. The company, having its headquarter in

Istanbul, serves through its 4 domestic cities and

Antwerp offices and a network of agencies spread over

189 countries. With its wide agency network throughout

the world, it continues to serve, with a sense of qualified,

reliable, and professional service supply and with its

wide agency connections, to many regions of Africa,

Europe, and America, especially to the Far East, Middle

East and Mediterranen Countries, in the areas of FCL full

container,LCL partial shipments, domestic

transportation, chartering, transit trade transportation,

andmcombined transportation.

(http://www.nmtlojistik.com/en)

NMT’s Vision: By changing the meaning of customer

and providing qualified, reliable, and affordable services,

to become the pioneering company of the forwarding

business. (http://www.nmtlojistik.com/en/vision)

Lean six sigma candidate selection is very important for

NMT Logistics, because the competition is very high in

the sector and NMT has a number of branches all over

the world. In addition, one of the strategies of NMT is to

increase productivity of the processes and to increase

customer satisfaction (including internal customer;

employees) by means of lean six sigma. The top

management committed this strategy and the vision and

the managers share them with the employees. The

company will start strategic projects to realize and to

deploy the strategy. A national funding and granting

organization supported the lean six sigma projects. Some

KPIs (Key performance indicator) are defined;

To reduce the lead times of the customer orders,

To reduce average cost per order,

To increase customer satisfaction,

To increase employee involvement and

satisfaction,

To reduce quality problems,

To reduce customer complaints.

NMT is a growing company, therefore they should define

its processes very carefully and make them in a

sustainable way. NMT bought personal computers and

new licenses for a statistical software package to be used

in lean six sigma projects for a better software and

hardware infrastructure. A domestic ERP which is

specific to logistics sector is used. In addition the firm

signed a contract to improve the ERP to gather

preliminary data from processes and to measure the

improvement and to see the progress of key performance

indicators. The ERP will be customized also according to

the specific needs of the processes and to get various

reports. It is obvious that if the digitalization of a

company is high, a company can get real, accurate, in

time, integrated data and related reports from ERP, CRM

and other software.

NMT preferred to hire an industrial engineer or an

industrial & system engineer, because NMT managers

believe that both theoretical and practical statistics

education is an advantage. After the interviews, four

candidates are eliminated. One candidate is eliminated

because he failed to the criterion “Successful References

in the Sector” after his former employer is called, one

candidate is eliminated according to the criterion “Too

high salary request” and two candidates are eliminated

to the criterion “Fluent in foreign language”.

Finally, two candidates are left for the application of

selecting the lean six sigma manager.




are found for a defined problem. Kahraman et al., (2014)

used trapezoidal interval type-2 fuzzy AHP method

together with a new ranking method for type-2 fuzzy sets

and applied the proposed method to a supplier selection

problem. In this paper, the trapezoidal interval type-2

fuzzy Analytic Hierarchy Process methodology is

applied for an industrial manager selection.

Definition 1: A trapezoidal interval type-2 fuzzy set can

be illustrated as below:

�̃̃�𝑖 = (�̃�𝑖𝑈; �̃�𝑖

𝐿)=(( 𝑎𝑖1𝑈 , 𝑎𝑖2

𝑈 , 𝑎𝑖3𝑈 , 𝑎𝑖4

𝑈 ;H1(�̃�𝑖𝑈), H2(�̃�𝑖

𝑈)), (

𝑎𝑖1𝐿 , 𝑎𝑖2

𝐿 , 𝑎𝑖3𝐿 , 𝑎𝑖4

𝐿 ;H1(�̃�𝑖𝐿), H2(�̃�𝑖

𝐿))) (1)

Where �̃� iU

is the upper membership function, �̃�iL is the

lower membership function; ai1U, ai2

U, ai3U, ai4

U, ai1L,

ai2L,ai3

L, and ai4L are the references points of the interval

type-2 fuzzy set �̃̃�i; Hj(�̃�iU) and Hj(�̃�iL) denote the

membership values of the trapezoidal membership

functions.

Step 1: Structure the decision-making problem as a

hierarchy as the first step in the crisp AHP approach.

After the goal has been set, criterion level should be

constructed. There might be sub-criterion or sub-sub-

criterion level as well, which should be constructed one

level below every time. The last level should be

constructed for the alternatives.


229

Figure 2: Hierarchy Structure

Step 2: This step is called prioritizing or weighting the

criteria, here all the criteria are compared and a pairwise

comparison matrix is constructed. Comparisons should

be made under the consideration of the goal (i.e. While

manager selection process, is sectoral experience more

important or educational level?). A linguistic matrix can

be constructed with the values as: AS, VS, FS, SS, E (can

be seen in table below). (If criteria A is very strong (VS)

with respect to criteria B, in the corresponding cell of the

matrix will get a value of “VS”. However, the cell

corresponding to criteria B w.r.t criteria A will get a

reciprocal element of “VS” (1/VS). (How to calculate

those values will be shown in another step.)

Applying Step 2:

Criteria Comparison Matrix

C1 C2 C3 C4

C1 E 1/SS FS VS

C2 SS E VS AS

C3 1/FS 1/VS E SS

C4 1/VS 1/AS 1/SS E

Step 3: With the same logic from criteria comparison

matrix described in step 2, alternative comparison

matrices will be constructed under the consideration of

each criterion (There will be 4 matrices if there are 4

criteria).

Applying Step 3:

Alternative Matrix 1 (in relation with Criteria1)

C1 A1 A2

A1 E 1/FS

A2 FS E


C2 A1 A2

A1 E SS

A2 1/SS E


C3 A1 A2

A1 E AS

A2 1/AS E


C4 A1 A2

A1 E 1/VS

A2 VS E

Step 4: Linguistic comparison matrices should be

converted to trapezoidal interval type-2 fuzzy sets’

numerical values as it is shown below.

Definition 2:

(𝑙𝑈, 𝑚1𝑈, 𝑚2𝑈, 𝑢𝑈; 𝛼𝑈, 𝛽𝑈)(𝑙𝐿 , 𝑚1𝐿 , 𝑚2𝐿 , 𝑢𝐿; 𝛼𝐿 , 𝛽𝐿)

AS Absolutely Strong

(7,8,9,9;1,1) (7.2,8.2,8.8,9;0.8,0.8)

VS Very Strong

(5,6,8,9;1,1) (5.2,6.2,7.8,8.8;0.8,0.8)

FS Fairly Strong

(3,4,6,7;1,1) (3.2,4.2,5.8,6.8;0.8,0.8)

SS Slightly Strong

(1,2,4,5;1,1) (1.2,2.2,3.8,4.8;0.8,0.8)

E Exactly Equal

(1,1,1,1;1,1) (1,1,1,1;1,1)

Cells with the reciprocal elements will be calculated as it

is described below:

Definition 3:

1/�̃̃� =(( 1

𝑎14𝑈 ,

1

𝑎13𝑈 ,

1

𝑎12𝑈 ,

1

𝑎11𝑈 ;H1(𝑎12

𝑈 ), H2(𝑎13𝑈 )), (

1

𝑎24𝐿 ,

1

𝑎23𝐿 ,

1

𝑎22𝐿 ,

1

𝑎21𝐿 ;H1(𝑎22

𝐿 ), H2(𝑎23𝐿 ))) (2)


230

Applying Step 4:

Table 1. Criteria comparison matrix

Step 5: The consistency check:

Step 5.1: The consistency should be checked for each

pairwise comparison matrices. In order to do that,

Defuzzified Trapezoidal Type-2 Fuzzy Set (DTraT)

approach, in defuzzification, will be used. (1)

Definition 4:

After applying the equation above for every fuzzy

number, there will be crisp numbered comparison

matrices (C). Those matrices will be used in order to find

the consistency ratios

Applying Step 5.1:

After applying DTraT method for every fuzzy number in

the criteria comparison matrix, we will get a new matrix

as seen below.

C1 C2 C3 C4

C1 1,00 0,45 4,75 6,65

C2 2,85 1,00 6,65 7,85

C3 0,21 0,14 1,00 2,85

C4 0,14 0,12 0,45 1,00

Alternative matrices do not need a consistency check,

since n=2, RI=0 which means the matrix is already

consistent.

Step 5.2: By eigenvector method used in all comparison

matrices, the crisp priority weights (w_i) will be

calculated. The eigenvector method is formulated below:

The columns of given matrix are summed. Every value in

a column will be divided by the calculated column’s sum.

This is made to normalize the crisp values.

Applying Step 5.2: Every cell value is divided by the sum

of the cells in each column.

C1 C2 C3 C4

C1 0,24 0,26 0,37 0,36

C2 0,68 0,59 0,52 0,43

C3 0,05 0,08 0,08 0,16

C4 0,03 0,07 0,03 0,05

Step 5.2: From the new matrix, each row’s average

values will be calculated and will be written as the

weight array (W).

Applying Step 5.2:

[

w1

w2

w3

w4

] = [

0,310,550,090,05

] (3)

Weight array will show the importance of the criteria as

C1 has an importance of 31%, C2 has 55%, C3 has 9%

and C4 has 5% of importance. It can be derived from this

result that personal and environmental analysis ability

(C2) is the most important criteria among all; leadership

property (C1) is more important than sectoral knowledge

(C3) and problem solving property (C4). Sectoral

knowledge (C3) and problem solving property (C4) are

very close in importance but sectoral knowledge is a

more appreciated property in this case.

Step 5.2: The firstly calculated crisp comparison matrices

(C) will be multiplied with their corresponding weight

arrays. A new array of C*W will be obtained.

Applying Step 5.2:

[

𝑎11 ∗ 𝑤1 + 𝑎12 ∗ 𝑤2 + 𝑎13 ∗ 𝑤3 + 𝑎14 ∗ 𝑤4

𝑎21 ∗ 𝑤1 + 𝑎22 ∗ 𝑤2 + 𝑎23 ∗ 𝑤3 + 𝑎24 ∗ 𝑤4

𝑎31 ∗ 𝑤1 + 𝑎32 ∗ 𝑤2 + 𝑎33 ∗ 𝑤3 + 𝑎34 ∗ 𝑤4

𝑎41 ∗ 𝑤1 + 𝑎42 ∗ 𝑤2 + 𝑎43 ∗ 𝑤3 + 𝑎44 ∗ 𝑤4

]=[

1,32,40,40,2

](4)

Step 5.2: CW array will be divided by the weight

array(W) by using matrix division. The resulted array is

eigenvector (W𝑖=[λ1, λ2 … ]) of the corresponding matrix.


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(Eigenvectors will be calculated for each matrix

separately.)

Applying Step 5.2:

Eigenvector of criteria comparison matrix

𝑐

𝑤= [

1,32,40,40,2

] / [

0,310,550,090,05

] = [

4,34,44,04,1

] = [

λ1

λ2

λ3

λ4

] (5)

Step 5.3: Average of eigenvalues will be calculated

(λ𝑜𝑟𝑡).

Definition 5:

λ𝑜𝑟𝑡 =λ1+ λ2+λ3+⋯+ λ𝑛

𝑛 (6)

Applying Step 5.3:

λ𝑜𝑟𝑡 =4,3+ 4,4+4,0+4,1

4 = 4,2 (7)

Step 5.4: Consistency Ratio (CR) and Consistency Index

(CI) will be calculated as below (RI is a pre-calculated

value and can be found in the table 2). CI value should be

smaller than 0.1, otherwise, corresponding matrix should

be constructed again.

Definition 6:

CR= λ𝑜𝑟𝑡− n

n−1 (8)

CI= 𝐶𝑅

𝑅𝐼 (9)

Table 2. Random Consistency Index n 2 3 4 5 6 7 8 9 10

RI 0.00 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.51

Applying Step 5.4:

CR= 4,2− 4

4−1 = 0,07 (10)

RI= 0,9 (11)

CI= 0,07

0,9 = 0,073 < 0,1 (12)

The criteria comparison matrix is consistent.

Step 6: Geometric mean of each row of type-2

fuzzy pairwise comparison matrices are

calculated as given below;

Definition 7:


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Step 7: Summation of the rows is required in order to

make normalization by dividing each row with the sum

result.

Definition 8:

�̃̃�𝑖=�̃̃�𝑖 ⊗ [�̃̃�1 ⨁ �̃̃�2 ⨁ �̃̃�3⨁ … ⨁ �̃̃�𝑛]−1 (13)

Summation between the trapezoidal interval type-2 fuzzy

sets;

Step 8: Construct a new Criteria-Alternative Matrix. For

each alternative row, multiply each value by its

corresponding criteria weight, then sum those values in

order to find the priority of that alternative. Those

calculations should be made for each alternative row. (In

order to control, the sum of priority values will be 1.)

By applying Step 8, results shown in table 3 are

calculated.

Step 9: Type-2 fuzzy and defuzzified overall weights of

the alternatives. By applying Step 9, results shown in

table 4 are calculated.


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Table 3. Criteria-Alternative Local and Global Weights Table

Table 4. Global Weights (Tyoe-2 fuzzy, Defuzzified, Normalized Crisp)

From the case results given above, it can be seen that in

the given comparisons, manager candidate A2 is a far

better choice with a 0,23 points comparing to the Lean

Six Sigma Manager candidate A1 with a 0,77 points.

4. CONCLUSION

The decision makers meet different factors when

deciding to select the most proper lean six sigma manager

candidate. If a wrong manager is selected, the decision

may affect the success of lean six sigma projects and the

motivation and moral of the related team members in the

organization. Business professionals and academics

believe that the process of personnel selection should be

on justice and with minimum subjectivity. Manager,

project management and six sigma techniques used for

the selected problem are very important for the success

of six sigma projects. This paper focuses the personnel

selection topic for lean six sigma, because improper

manager may focus wrong priorities and cannot use the

right techniques.

The selection of the lean six sigma manager may be a

different one under the different situations. The

originality of the paper is using type 2 fuzzy multi criteria

decision making to select the best lean six sigma

candidate manager. In addition, some criteria are defined

to eliminate improper candidates such as “Successful

References in the Sector”, “Too high salary request” and

“Fluent in foreign language” before the application of

MCDM method. Since the problem of selection of lean

six sigma manager has various and conflicting criteria, it

is a Multi Criteria Decision Making problem. Fuzzy AHP

is used very commonly, because it can reflect human

thinking style, whereas classical AHP cannot reflect

properly. The trapezoidal interval type-2 fuzzy Analytic

Hierarchy Process methodology, which is one of the most

used methods, is applied for an industrial manager

selection. The membership functions of type-1 fuzzy sets

are crisp; therefore, they cannot model uncertainties

directly. Nevertheless, the membership functions of type-

2 fuzzy sets are fuzzy, they can model uncertainties. The

framework of the study is:

Collect Information about the Candidates of

Lean Six Sigma Manager position,

Eliminate improper Candidates according to the

defined criteria,

Form type 2 Fuzzy AHP Method

Apply type 2 Fuzzy AHP Method

Make the Final Decision

After the evaluations of decision makers and a literature

review, 4 criteria are used. Some candidates are

eliminated according to the rules defined in the approach,

then 2 candidates are compared. Interval type-2 fuzzy

sets represent uncertainties, better. Firms can use the

methodology when attempting to select both lean six

sigma managers and other managers. The lessons learnt

from this logistics firm case or other applications can be

added into the knowledgebase of a decision support

system. As a further research, some sensitivity analysis

can be done and other MCDM methods can be applied

and their performances can be compared.


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Ufuk Cebeci Istanbul Technical Univercity,

Istanbul,

Turkey

[email protected]


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